Breaking Symmetries - Computer Science > Logic in Computer Science

Abstract: A well-known result by Palamidessi tells us that {\pi}mix the {\pi}-calculuswith mixed choice is more expressive than {\pi}sep its subset with onlyseparate choice. The proof of this result argues with their differentexpressive power concerning leader election in symmetric networks. Later on,Gorla of- fered an arguably simpler proof that, instead of leader election insymmetric networks, employed the reducibility of -incestual- processes mixedchoices that include both enabled senders and receivers for the same channelwhen running two copies in parallel. In both proofs, the role of breaking ini-tial symmetries is more or less apparent. In this paper, we shed more light onthis role by re-proving the above result-based on a proper formalization ofwhat it means to break symmetries-without referring to another layer of thedistinguishing problem domain of leader election.Both Palamidessi and Gorla rephrased their results by stating that there isno uniform and reason- able encoding from {\pi}mix into {\pi}sep . We indicatehow the respective proofs can be adapted and exhibit the consequences ofvarying notions of uniformity and reasonableness. In each case, the ability tobreak initial symmetries turns out to be essential.